Geodesic
Multivalued Homotopy on an Ordered Set, Fixed and Coincidence Points of Mappings, and Applications in Game Theory
Matematičeskie zametki, Tome 106 (2019) no. 4, pp. 565-577

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The article develops results of the authors' previous papers on the topic. The notion of the homotopy of a multivalued mapping of an ordered set is introduced. We study the problem as to whether the existence of a fixed point (or a coincidence point) is preserved under multivalued homotopies of a multivalued mapping (or a pair of multivalued mappings). An application of some of the authors' previous results on fixed points in game theory is considered.
Keywords: ordered set, multivalued homotopy, fixed point, coincidence point, pair of equilibrium strategies. 
@article{MZM_2019_106_4_a7,
     author = {D. A. Podoprikhin and T. N. Fomenko},
     title = {Multivalued {Homotopy} on an {Ordered} {Set,} {Fixed} and {Coincidence} {Points} of {Mappings,} and {Applications} in {Game} {Theory}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {565--577},
     publisher = {mathdoc},
     volume = {106},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a7/}
}
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D. A. Podoprikhin; T. N. Fomenko. Multivalued Homotopy on an Ordered Set, Fixed and Coincidence Points of Mappings, and Applications in Game Theory. Matematičeskie zametki, Tome 106 (2019) no. 4, pp. 565-577. http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a7/